"Arens regularity of the Orlicz Fig\`a-Talamanca Herz Algebra"Dabra, ArvishLet G be a locally compact group. The $p$-version ($1<p<\infty$) of the Fourier algebra is called as Fig\`a-Talamanca Herz algebra and is denoted by $A_p(G).$ For $p=2,$ $A_p(G)$ coincides with the Fourier algebra $A(G).$ It is well known that Orlicz spaces are the natural generalization of the classical $L^p$-spaces. Let $A_\Phi(G)$ be the Orlicz-version of the Fig\`{a}-Talamanca Herz algebra of G associated with a Young function $\Phi.$ As Arens regularity is an important tool to study groups with the help of certain Banach algebras related to it; we show that if $A_\Phi(G)$ is Arens regular, then $G$ is discrete. This generalizes the result by Forrest about the Arens regularity of the $A_p(G)$ algebras. We also show that $A_\Phi(G)$ is finite-dimensional if and only if $G$ is finite. Further, for amenable groups, we show that $A_\Phi(G)$ is reflexive if and only if $G$ is finite, under the assumption that the associated Young function $\Phi$ satisfies the MA-condition. |
| https://ps-mathematik.univie.ac.at/e/talks/strobl24_Dabra_2024-02_Abstract.pdf |
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